I use cardboard for my cards. not sure where I got it, but it isn't the corrugated kind, it is nice sturdy pieces. But moving around my boards I've had a card come off on occasion. One time I was trying to get guys off the bench after warmups at a hockey game. Card fell down in the tunnel. Thankfully there was a nice trainer/someone to pick it up for me. Was a team set card to.
Corner I had on it was due for a replacement. So shuffling things around you definitely could risk a card falling off the board even if they are secured with the photo corners.

those artist sketch book s are only a few dollars at walmart. they have nice thick covers so your cards get some protection. I have had my photo corners on there since 2008 and have not replaced a single one. The pages are thick and sturdy and allows me to alphabetize the cards for quick access. I highly recommend it.